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Math Help - function composition problem

  1. #1
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    Post function composition problem

    Let h be defined as h(x) = \sqrt{\sqrt{(x-3-9)}}. Express h as a composition f \circ g. Identify f and g and state the domain and range of each of h, f and g.

    Thanks guys.
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  2. #2
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    Are you sure about the argument under the radical? It seems a little odd.

    Actually, x - 3 - 3 would make it more fun.

    Anyway, try f(x) = \sqrt{x} and g(x) = x - 3 - 9. This gives f(f(g(x))) = h(x). Or we could have r(x) = x - 3 and get f(f(g(g(g(g(x)))))). Okay, I'm having too much fun.
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  3. #3
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    hey sorry bout the late reply..internet was down after moving house

    its meant to be

    h(x) = \sqrt{\sqrt{(x-3}-9)}.

    cheers
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  4. #4
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    Quote Originally Posted by smplease View Post
    hey sorry bout the late reply..internet was down after moving house

    its meant to be

    h(x) = \sqrt{\sqrt{(x-3}-9)}.

    cheers
    One obvious possibility is f(x) = \sqrt{x} and g(x) = \sqrt{x - 3} - 9. I hope you see why.

    There is another possibility, left for you to find.
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